Let \({R}=\lbrace wsw^{-1}|w\in W^v, s\in {S}\rbrace \) be the set of reflections of \(W^v\) . Let \(r\in {R}\) . Write \(r=wsw^{-1}\) , where \(w\in W^v\) , \(s\in {S}\)  and \(ws>w\)  (which is possible because if \(ws<w\) , then \(r=(ws)s(ws)^{-1}\) ). Then one sets \(\alpha _r=w.\alpha _s\in \Phi _+\) (resp. \(\alpha _r^\vee =w.\alpha _s^\vee \in \Phi ^\vee _+\) ). Conversely, if \(\alpha \in \Phi \)  or \(\alpha ^\vee \in \Phi ^\vee \) , \(\alpha =w.\alpha _s\)  or \(\alpha ^\vee =w.\alpha _s^\vee \) , where \(w\in W^v\)  and \(s\in {S}\) , one sets \(r_{\alpha }=wsw^{-1}\)  or \(r_{\alpha ^\vee }=wsw^{-1}\) . This is independant of the choices of \(w\)  and \(s\)  by [1]}.
